Google Inc. will cut about 4,000 jobs at its Motorola Mobility Holdings Inc. unit, or 20 percent of the staff at the company it bought for about $12.5 billion.

Two-thirds of the reductions will be outside the U.S., the Mountain View, California-based company said in a regulatory filing today. Google will also shut down about one-third of Motorola Mobility’s 90 facilities and simplify its wireless product portfolio, it said. Google said the measure will incur severance-related costs of no more than $275 million.

Larry Page, who became the chief executive officer of Google last year, is streamlining the company as it pushes into the hardware market. Google, owner of the world’s most-popular search engine, completed the takeover of Motorola Mobility in May in its biggest takeover, boosting its patent portfolio and stepping up competition with competitor Apple Inc.